------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 加精了\tiny 加精了加精了 本篇讲解哈希算法，这是一种在很多领域都有运用的算法。 > 目录 > > > > 1.简介 > > > > > > 2.关键性质 > > > > > > 3.核心思想 > > > > > > 4.单哈希算法 > > > > > > 5.双哈希算法 > > > > > > 6.无符号长整型溢出法 > UPD 10.5，增加随机模数哈希算法。 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ PART 1. 简介 哈希算法在编程竞赛中的主要应用是把一个字符串映射为一个数字（通常会取模）来把O(n)O(n)O(n)的字符串比较问题转化为O(1)O(1)O(1)的数字比较（当然预处理不是O(1)O(1)O(1)的）。 PART 2. 关键性质 哈希算法主要有以下性质 1. 确定性 * 相同的输入必定产生相同的哈希值（也是哈希算法的基础） 2. 高效性 * 计算哈希值的过程应该很快 3. 雪崩效应 * 输入的微小变化会导致输出的巨大差异 * 例如"aelloaelloaello"和"hellohellohello" 的哈希值应该完全不同 4. 抗碰撞性（这个指标是用来判定哈希冲突的） * 弱抗碰撞性：给定一个输入，很难找到另一个不同的输入产生相同的哈希值 * 强抗碰撞性：很难找到任意两个不同的输入产生相同的哈希值 PART 3. 核心思想 哈希算法的核心思想在于，将字符串的每个字符对应成0~25的数字，再将整个字符串映射为一个kkk进制数（kkk通常取128128128）模一个大质数（比如1e91e91e9、998244353998244353998244353）。 具体实现不难，只需预处理128128128的幂次就可以轻松实现。 PART 4. 单哈希算法 单哈希算法即只用一个数作为模数。 实现并不难，模板代码就不给了，给出一道例题 PART 5. 双哈希算法 这是我们重点讲解的算法。 要想学习双哈希算法我们首先得了解—— 哈希冲突\HUGE 哈希冲突哈希冲突 相信很多读者会发现：哈希算法是基于映射和取模的，那岂不是很好hackhackhack？只要构造两个取模后相等的字符串不就好了？没错，这就是哈希冲突，双哈希算法就是用以解决哈希冲突的。 那么我们如何解决哈希冲突呢？很粗暴，就是用两个不同的模数来判断，如果两个字符串所映射的数字模两个数都相等，那么他们大概率就是相等的。 但是！\HUGE 但是！但是！ 这时候，聪明的同学就说了，主包主包，那还是可以hackhackhack啊？没错，如果你采用固定模数，别说双哈希，哪怕是十哈希也没有用！ 所以！\HUGE 所以！所以！ 我们一般使用随机模数哈希！ > 注：一个实用技巧，哈希在实战中常常使用前缀的形式，详见后面的代码。 下面给出一道例题 代码（固定模数）： 我在其中封装了两个哈希结构，不会封装的也可以分开写。 PART 6. 无符号长整型溢出法 双哈希固然好用，但是实现非常困难也没多困难，所以，我们隆重推出懒人写法—— 无符号长整型法，即unsignedunsignedunsigned longlonglong longlonglong。 这个算法基于无符号长整型溢出后自动取模的特点，但是有小概率被卡CSP被卡别怪我 还是给一道例题 代码： ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 大概是史上最短创作计划了，萌新有什么看不懂的可以在评论区留言，也欢迎大佬给出珍贵的建议，@AC君求精。

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舍门 第一章：初入迷雾 第二章：无人别墅区 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 诡异之门 第一章：入门+第二章：惩罚 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 番外 诡异之门番外#1 舍门番外#1 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 故事的梗概 萧秋水意外进入了诡舍，在很多人的帮助下，他虽然打开了迷雾世界的终点，但失去了那些帮助他的人，而且他也不是曾经的他了…… ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 读者 什么时候开始读 新手小小白 2025-07-14 17:04 ༺ཌༀ我要上南开ༀད༻ 2025-07-13 17:40 进团也提前可以观看 1.南开大学 2.超级大帅哥 3.C++知识练习（复习+自习室） 4.北欧联邦同盟国 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 彩蛋 （第三章我在搞） 暂无 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 问答 暂无

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该算法能过不亚于 n2n^2n2 过百万。

https://www.acgo.cn/problemset/info/79834 能做出来代表****** 已经死了

https://www.acgo.cn/problemset/info/79834 能做出来代表****** 已经死了

https://www.acgo.cn/problemset/info/79834 能做出来代表****** 已经死了

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沙发

输入一个 8×88\times88×8 的 .Q.Q.Q 矩阵，试试结果

给个关吧！乞讨ing!

我事皮柴！！！

这是一个非常NB的材质包 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ 不仅有鸡哥 还有小猪佩奇 帅气的超人弱 不知名村民 不知名铁傀儡 还有牢大 海绵bb 热情的国宝 巴嘎雅路的沸羊羊桑 还有想看的私信 陶源 注：此材质包不为陶源所创

有狂野飙车9的玩家吗？在线等！！！！！

#include<bits/stdc++.h> using namespace std; const int N=1e5+10; int a[N]; long long sum=0; int main(){ int n,x; cin>>n; for(int i=1;i<=n;i++)cin>>a[i]; cin>>x; for(int i=1;i<=x;i++)sum+=a[i]; cout<<sum; return 0; }